This paper focuses on the combinatorial enumeration of truncated hollow standard Young tableaux approximate C shape. The formula approximately C-shaped SYT, namely convolution Catalan numbers, is derived by using multi-integral method based sequence statistical model. Meanwhile, it found that first and last rows differ in number boxes. In case where boxes row n large enough, SYT does not change...

Catalan words are particular growth-restricted counted by the eponymous integer sequence. In this article we consider avoiding a pair of patterns length 3, pursuing recent initiating work first and last authors S. Kirgizov where (among other things) enumeration 3 is completed. More precisely, explore systematically structural properties sets under consideration give enumerating results means re...

Transfer systems are combinatorial objects which classify N∞ operads up to homotopy. By results of A. Blumberg and M. Hill [2], every transfer system associated a linear isometries operad is also saturated (closed under particular two-out-of-three property). We investigate isometric with equivariance group Cpmqn, the cyclic order pmqn for p,q distinct primes m,n≥0. give complete enumeration Cpm...

Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds: cycle covers, closed walks, spanning trees. We show that if the weights of the edges of the graph are within a constant factor, fixed in advance, of each other t...

A novel approach for the multidimensional scaling of large combinatorial libraries is presented. The method employs a multilayer perceptron, which is trained to predict the coordinates of the products on the nonlinear map from pertinent features of their respective building blocks. This method limits the expensive enumeration and descriptor generation to only a small fraction of products and, i...

The maximum number of minimal dominating sets that a graph on n vertices can have is known to be at most 1.7159. This upper bound might not be tight, since no examples of graphs with 1.5705 or more minimal dominating sets are known. For several classes of graphs, we substantially improve the upper bound on the maximum number of minimal dominating sets in graphs on n vertices. In some cases, we ...

We give an algorithm for enumerating cosets of a group defined as a finite homomorphic image of a semi-direct product of free products of cyclic groups by a group of monomial automorphisms. Lots of finite groups, including some of the sporadic simple groups can be defined in this mannar. Mathematics Subject Classification: 20Bxx

Planetary gear trains (PGTs) are used in a wide range of mechanical applications. Graphs to represent PGTs. PGTs classified into single-planet and multi-planet depending on the number vertices second level graph. In this paper, novel method for synthesizing up is developed. The first step synthesis process enumeration spanning trees. A combinatorial analysis then obtain link assortment arrays c...

A variety of software packages are available for the combinatorial enumeration of virtual libraries for small molecules, starting from specifications of core scaffolds with attachments points and lists of R-groups as SMILES or SD files. Although SD files include atomic coordinates for core scaffolds and R-groups, it is not possible to control 2-dimensional (2D) layout of the enumerated structur...

Given a combinatorial search problem, it may be highly useful to enumerate its (all) solutions besides just finding one solution, or showing that none exists. The same can stated about optimal if an objective function is provided. This work goes beyond the bare enumeration of and addresses computational task solution by optimality (SEO). studied in context Answer Set Programming (ASP) where (op...